2011 MJC P1 Q7 (i)(ii)

The lines \({{l}_{1}}\) and \({{l}_{2}}\) have equations \(\mathbf{r}=\overrightarrow{OA}+\lambda \left( \begin{matrix} 1 \\-1 \\5 \end{matrix} \right)\) and \(\mathbf{r}=\overrightarrow{OB}+\mu \left( \begin{matrix} 2 \\1 \\ 1 \end{matrix} \right)\), \(\lambda \), \(\mu \in \mathbb{R}\) respectively, where \(\overrightarrow{OA}=\left( \begin{matrix} 1 \\ 2 \\ -1 \end{matrix} \right)\), \(\overrightarrow{OB}=\left( \begin{matrix} 2 \\ 4 \\-5 \end{matrix} \right)\). The lines \({{l}_{1}}\) and \({{l}_{2}}\) intersect at point \(C\).

1. Find the position of vector of \(C\).[3]
2. Given that \(\overrightarrow{AB}\) is perpendicular to \({{l}_{2}}\), find the equation of the reflection of \({{l}_{1}}\) in \({{l}_{2}}\).[4]